That article contains some blatanly wrong statements, I woulnd't consider it trustworthy at all. 25 Tesla is not the strongest magnet in existence (see e.g. a 45 Tesla hybrid magnet built in 1999‌​). Those high-field magnets usually have a very small bore, so you can't put a human into the maximal magnetic field of the magnet, as there's just not enough space inside.
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Mad Scientist♦Nov 24 '12 at 14:41

@MadScientist: Thanks, the question is updated to be more to-the-point now
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EveryoneNov 24 '12 at 14:52

I don't think you need to remove that part, I just wanted to point out the errors in the linked article
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Mad Scientist♦Nov 24 '12 at 15:20

2 Answers
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First thing comes to my mind is the Hall effect. Any directional ion or electron flow will experience a force (depending on the orientation with respect to the magnetic field). So if the magnet is very strong, I think some of the ion channels for action potential generation and propagation would malfunction. (11 mT stopped action potentials for a while but recovered in mouse as reported here.)

However, according to thesepapers static magnetic fields has little biological effect, and it seems to be reversible. But, this reports genotoxicity in 4.5T (in vitro), and developmental disorders in 1.5T (in vivo, mouse). Contradictory reports indicate we do not know the full answer yet as usual.

"Strong" is en entirely relative term, but given the number of MRI's performed, its pretty clear that fields several orders of magnitude larger than the Earth's background 0.5 gauss are at least "mostly harmless" with an exposure of limited duration.

There are no known harmful side-effects associated with temporary exposure to the strong magnetic field used by MRI scanners. However, there are important safety concerns to consider before performing or undergoing an MRI scan.

This article describes human brain imaging with a 9.4T instrument, although this is about 10x larger than the strength of most MRIs. Note that "no detrimental effects" does not mean zero effects, but this is starting to get into the range of the 25T described above. There are 20T+ MRI machines avaialble, but I could not find an article describing use on live organisms. There is just this one on dead mice parts.